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<title>Mesh Generation</title>

<h1>Guaranteed-Quality Mesh Generation</h1>
<h2><!WA0><!WA0><!WA0><!WA0><a href=http://www.cs.cornell.edu/Info/People/chew/chew.html>Paul Chew</a></h2>
<hr>

My work on mesh generation has been motivated by the finite element
method, a widely used technique to obtain approximate solutions to
partial differential equations.  The first step of this method is to
divide the given problem region into simply-shaped elements creating a
mesh.  A number of algorithms have been developed to automate this
process, but most of these algorithms do not provide a guarantee about
the quality of the resulting mesh (for instance, an element may cross a
region boundary or there may be some flat triangles leading to poor
error bounds).  I have developed efficient techniques for producing
meshes of guaranteed quality for problems in the plane and for curved
surfaces:  the elements produced are all triangles that are close to
equilateral in shape, all region boundaries are respected, and the user
can control the element density, producing small elements in
``interesting'' regions and large elements elsewhere.  I am working to
extend this technique to full three-dimensional problems, producing
tetrahedral meshes. <p>

<!WA1><!WA1><!WA1><!WA1><a href=http://www.cs.cornell.edu/Info/People/chew/2d-mesh.eps>Example 2D Mesh.</a><p>

<!WA2><!WA2><!WA2><!WA2><a href=http://www.cs.cornell.edu/Info/People/chew/surface-mesh.eps>Example Surface Mesh.</a><p>

<!WA3><!WA3><!WA3><!WA3><a href=http://www.cs.cornell.edu/Info/People/chew/animation.eps>The Mesher in Action.</a> A postscript animation
of the mesher at work.  The colors represent grades for the various
triangles: red implies bad shape, yellow implies too large, blue
implies boundary is too long, and green implies all right. <p>

<!WA4><!WA4><!WA4><!WA4><a href=http://simlab.cs.cornell.edu/demonstrations/mesher.html>An
Interactive Meshing Demo.</a> Mesh a polygonal shape of your own
choosing.  The input for this is currently very slow; the whole demo
is still being modified.

<h2>Some References</h2>

L. Paul Chew, ``Guaranteed-Quality Mesh Generation for Curved Surfaces,'' 
<i>Proceedings of the Ninth Symposium on Computational Geometry</i>
(1993), ACM Press, 274-280.<p>

L. Paul Chew, <i>Guaranteed-Quality Triangular Meshes</i>, <!WA5><!WA5><!WA5><!WA5><A
HREF=http://cs-tr.cs.cornell.edu:80/TR/CORNELLCS:TR89-983?abstract=>
Department of Computer Science Tech Report 89-983</A>, Cornell
University (1989).<p>
